My boyfriend is filing head of household and claiming me and my daughter.. He made roughly 45,000 last year? Around how much can we expect to get back?

Your b/f can claim you dependent (as Qualifying Relative) only if
1. You lived with him/her all the year,
2. you did not earn more than $3,500 in 2008, and
3. your relationship does not violate local law. Read : Your U.S. Tax Return: Requirements for claiming a dependent (http://taxipay.blogspot.com/2008/03/requirements-for-claiming-dependent.html)

Further, your daughter must have lived in his house the entire year to be considered a "qualifying person" for dependency and HoH purposes.

Your b/f can claim you dependent (as Qualifying Relative) only if
1. You lived with him/her all the year,
2. you did not earn more than $3,500 in 2008, and
3. your relationship does not violate local law. Read : Your U.S. Tax Return: Requirements for claiming a dependent (http://taxipay.blogspot.com/2008/03/requirements-for-claiming-dependent.html)

Yes, I have lived with him the entire year and was umemployeed, Our daughter has lived with us the entire year as well

Okay, because she is a qualifying person, not a qualifying child, your boyfriend CAN claim you and her as dependents, but he CANNOT qualify for the $1,000 Child Tax Credit.

Under those conditions, his tax liability on $45K in income is $4,599. I cannot say what his refund will be because I do not know how much was withheld. He made too much money to qualify for the Earned Income Credit (EIC).

However, YOU may have unemployment compensation that is taxable income. If it exceeds $3,500, then your boyfriend CANNOT claim you. Unemployment compensation does NOT qualify you for the EIC, so allow him to claim your daughter in any event.